1. Field of the Invention
The present invention relates to a decoding method for decoding code words that are wordwise protected by a non-binary BCH code against at least one symbol error. In most practical codes, each symbol contains a string of at least two bits. More generally, however, the cardinality of the symbol set is at least three. The invention is applicable to non-primitive BCH-codes as well as to primitive BCH-codes. In a primitive code the code length is exactly (2.sup.n-1). In a non-primitive code the length can be any odd integer, the code being nevertheless still a well at to non-narrow-sense BCH-codes. The invention is applicable to full-length codes as well as to shortened or punctuated BCH-codes. All these exemplary sub-categories are considered well-known in the art and will not be explained in detail. The derivation hereinafter will only be given for one particular sub-category, to wit, a primitive, narrow-sense BCH-code. Extension to more general BCH-codes is straightforward. A further sub-category of BCH-codes are Reed-Solomon codes, wherein the finite field associated with the code symbols and the finite field for the decoding calculations are identical. In contradistinction thereto, the code symbols may also be defined as a sub-field of the field that is used for the calculations. The present invention applies to both categories. As far as the invention is concerned, the symbols have more than two possible values, which means that localizing an error also necessitates finding the error value. As used herein and in the ensuing claims, the term "error value" refers to the symbol value to be included in a decoding code word at a location therein ("error location") at which a symbol error is present in the received code word being decoded. The invention particularly suits codes that have a high distance, and thus could, in principle, correct many symbol errors in each code word.
2. The Generally Related Art
A particular method according to the above foregoing has been disclosed in U.S. Pat. No. 4,642,808 assigned to the same assignee. The code therein is a distance 21 code using 8-bit symbols, and is a Reed-Solomon code. Such method, while improving on classical correction methods by in particular accelerating the decoding for a low number of symbol errors, still requires a rather long processing time and/or the use of complicated or special purpose hardware, when for example more than three errors occur.